The control of highly infectious diseases of livestock such as classical swine fever, foot-and-mouth disease, and avian influenza is fraught with ethical, economic, and public health dilemmas. Attempts to control outbreaks of these pathogens rely on massive culling of infected farms, and farms deemed to be at risk of infection. Conventional approaches usually involve the preventive culling of all farms within a certain radius of an infected farm. Here we propose a novel culling strategy that is based on the idea that farms that have the highest expected number of secondary infections should be culled first. We show that, in comparison with conventional approaches (ring culling), our new method of risk based culling can reduce the total number of farms that need to be culled, the number of culled infected farms (and thus the expected number of human infections in case of a zoonosis), and the duration of the epidemic. Our novel risk based culling strategy requires three pieces of information,

Epidemics of infectious diseases such as classical swine fever, food-and-mouth, and avian influenza continue to wreak havoc in commercial livestock [

The aim of preventive culling in outbreaks of commercial livestock is to contain the epidemic by removing susceptible flocks in the vicinity of infected farms; a typical strategy used for this is ring culling. In this strategy all farms within a certain radius of an infected farm are culled, typically starting close to the infected farm(s). The distance to an infected farm is related to the probability of a farm becoming infected. Ring culling therefore essentially involves culling the farms with the highest probability of becoming infected. We argue that, in addition to the distance to infected farms, another factor that is important is the local density of neighbouring farms. The local density determines how an epidemic is likely to develop, e.g.: a farm in an area with high density will likely cause more new infections than a farm in area with a low density; this implicitly follows from the relationship between distance and risk. In previous work the number of new infections that each infected farm is expected to cause was quantified by a farm reproduction number (R) and they were used to create risk maps that indicated areas with potential for high epidemic spread [

In this paper a novel culling strategy is introduced that takes into account not only the distance of susceptible farms to the infected farms, but also the number of secondary infections that a susceptible farm is expected to produce should it become infected. Specifically, we calculated for each farm not yet (known to be) infected a so-called risk value, which represents the number of infections the farm is expected to produce given current information on the unfolding of the epidemic. We argue that farms which rank highest in the risk based ordering should be culled first, thereby achieving an efficient allocation of resources (i.e. time, money, equipment). In practice, the risk value of each susceptible farm is given by the probability that a farm will become infected in a certain time span multiplied by the reproduction number of the farm once it is infected. Similar ideas that incorporate the connectivity of farms or individuals in applying an intervention measure have been suggested before in (non-spatial) network models of infectious disease spread [

Our risk based culling scheme works with three pieces of information. First the locations of all farms in the area at risk need to be known. Second, an assessment of the current state of the epidemic should be available, in particular which farms are infected, and which farms are still susceptible. Third, an estimate of how the transmission probability depends on the distance between infected and susceptible farms should be at hand. The first two pieces are usually readily available during an epidemic. For the third piece of information estimates from past epidemics can usually be used [

We evaluate the performance of the risk based culling strategy in a simulation study that is loosely based on a large outbreak of highly pathogenic H7N7 avian influenza in the Netherlands. Parameter values and the transmission hazard are based on experience with this outbreak [

The spread between farms was modelled with a stochastic SEIR model (Susceptible-Exposed-Infected-Removed) that operates with fixed time steps of 1 day. The probability _{i }

where _{i}(t)

The function _{ij}) _{ij }

Although it is our goal to investigate the efficiency of risk based culling strategies in general, the parameters are specifically tailored to mimic the spatial spread of highly pathogenic avian influenza viruses in densely populated poultry areas. The shape of the hazard and estimates of the parameters to scale the hazard were estimated from the outbreak of highly pathogenic H7N7 avian influenza in the Netherlands [

where _{0}, r_{0}

Settings of the hazard kernel (equation 3) as used in the base scenario and the scenarios of the sensitivity analyses

Base hazard kernel | h_{0} | 0.0016 |
---|---|---|

r_{0} | 1.9 | |

α | 2.1 | |

Increased R0 | h_{0} | 0.0020 |

Decreased R0 | h_{0} | 0.0012 |

Increased tail | h_{0} | 0.0009 |

r_{0} | 1.9 | |

α | 1.4 | |

Decreased tail | h_{0} | 0.0023 |

r_{0} | 1.9 | |

A | 2.8 | |

Increased clustering | h_{0} | 0.0012 |

Decreased clustering | h_{0} | 0.0020 |

Misspecified kernel | 0.00028 |

Only the modifications of the base scenario are shown. For the scenario with the misspecified kernel, the hazard is constant.

We assume that upon infection each farm first becomes exposed (i.e. infected but not yet infectious) for a period of two days (Figure

We now define in more detail the two culling strategies considered in this paper: ring culling and risk based culling. With ring culling all farms within a certain radius of any of the farms where an infection was detected are preventively culled. Culling is then continued until there are no more farms present in any of the (possibly overlapping) rings around infected farms. Ring culling is typically carried out inside-out, i.e. starting near the infected farm on the inside of the ring. In our model this is mimicked by consistently selecting the farm that is closest to a farm where an infection has been detected. An alternative ring culling strategy works from the outside of the ring to the inside. The rationale for this strategy is that it may help contain the infection within the culling ring. In this strategy the farm that is furthest away (but within the ring) of any farm where an infection was detected is culled first. In The Netherlands in 2003 culling was started on the inside of the ring close to the infected farms. At the start of the epidemic a 1 km ring was used, and later in the epidemic 3 km rings were used. In our analysis we consider both these radii. In our calculations for outside-in ring culling we considered a scenario with a ring radius of 3 km.

With risk based culling the estimated number of infections each farm is expected to create is used as culling criterion. The candidate farm with the highest expected number of new infections is then preventively culled first. The expected number of infections _{i }_{i}_{i}

Assuming a gamma distributed infectious period with mean _{i}

where

The exact probability for a farm to become infected (_{i}_{jd}_{i}*

_{jd }= 7, and T = 7 which results in 5 days exposure.

The hazard is approximate (as indicated with the *) because farms that are infected but have not been yet been detected are not taken into account because these are unknown at that point in time. The approximate probability (_{i}*

This probability is used to calculate the approximate expected number of infections caused by farm

The efficiency of various conventional ring culling strategies and the novel risk based culling strategy were assessed using simulations of outbreaks on maps with randomly generated farm locations (see Additional file

To prevent early stochastic fade-out, and to condition on a large epidemic, all simulations were seeded with 10 infectious and 10 exposed farms (Figure

In a future epidemic the exact shape of the hazard kernel of the disease spread is likely to be unknown. We therefore tested the sensitivity of the results to changes in the hazard kernel (Table

The relevant outputs of the model are the total number of farms culled, the number of infectious farms culled, and the duration of the epidemic (defined as the time from the first detection until the last culling of an infected farm). The total number of farms that are culled and the duration of the epidemic are both measures with economic relevance, not only because of the direct costs of culling, but also because under EU regulations borders will be closed for export during (an for some period after) an epidemic of avian influenza. Furthermore, minimizing animal suffering in itself is a worthy goal. The number of farms that are culled while being infectious is relevant because it determines the level of human exposure to an agent with zoonotic potential [

The simulation results obtained contain three sources of variation, i.e. (1) the culling strategy, (2) the random maps, and (3) the stochastic epidemic process. To separate these variances, and to single out the effect of the culling strategy, we analyzed the simulation results with a linear mixed model that used the maps as a random effect and the culling strategy as a fixed effect. The mixed model was used to estimate confidence bounds for the effect of the various culling strategies.

Risk based culling reduced the number of infected farms culled compared to both 1 and 3 km ring culling strategies, and thereby should be able to reduce the number of human infections (Table

Simulation results for the various risk based and ring culling strategies in the base scenario

Culling strategy | Culled infected | Total farms culled | Epidemic in days | |||
---|---|---|---|---|---|---|

Risk based, thresh = 0.001 | 216 | (194;239) | 958 | (920;971) | 57 | (58;59) |

Risk based, thresh = 0.0005 | - | (- | - | (- | ||

Risk based, thresh = 0.005 | (- | - | (- | |||

Risk based, thresh = 0.001/3 km ring^{1)} | (- | - | (- | |||

Ring 1 km, In - > Out ^{2)} | ||||||

Ring 3 km, In - > Out ^{3)} | (- | |||||

Ring 3 km, Out - > In |

Brackets indicate 95% confidence interval.

The results of "Risk based, thresh = 0.001" with confidence bounds were estimated as the intercept of a mixed model that incorporated maps as a random effect and culling strategy as a fixed effect. The "+" or "-" for the alternative strategies indicate the difference compared to "Risk based, thresh = 0.001". Confidence bounds for the alternative strategies are also around the difference.

^{1) }Risk based culling in a 3 km ring.

^{2) }In - > Out: culling starts with farms that are closest to the infected farm.

^{3) }Out - > In: culling starts with farms within the ring that are farthest from the infected farm.

Overview of results obtained with various scenarios used in the sensitivity analysis

Scenario | Culling strategy | Culled infected | Total farms culled | Epidemic in days | |||
---|---|---|---|---|---|---|---|

Decreased capacity | Risk, thresh = 0.001 | 374 | (329;420) | 996 | (964;1027) | 72 | (71;74) |

Ring 1 km, In - > Out ^{1)} | |||||||

Ring 3 km, In - > Out ^{2)} | |||||||

Increased capacity | Risk, thresh = 0.001 | 161 | (145;176) | 1064 | (1038;1090) | 47 | (46;47) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Increased R0 | Risk, thresh = 0.001 | 460 | (412;507) | 1250 | (1224;1276) | 65 | (64;66) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Decreased R0 | Risk, thresh = 0.001 | 100 | (91;110) | 798 | (771;825) | 44 | (43;45) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Increased tail | Risk, thresh = 0.001 | 183 | (169;197) | 1076 | (1050;1103) | 59 | (58;60) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Decreased tail | Risk, thresh = 0.001 | 220 | 193;247 | 958 | (986;929) | 50 | (49;51) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Less clustering | Risk, thresh = 0.001 | 191 | (175;206) | 1003 | (983;1023) | 55 | (54;56) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

More clustering | Risk, thresh = 0.001 | 277 | (222;332) | 1127 | (1079;1176) | 57 | (55;59) |

Ring 1 km, In - > Out | |||||||

Ring 3 km, In - > Out | |||||||

Misspecified kernel | Risk, thresh = 0.001 | 255 | 1095 | 59 | |||

Ring 1 km, In - > Out | +24 | +19 | +4 | ||||

Ring 3 km, In - > Out | +25 | +397 | +1 |

Brackets indicate 95% confidence interval.

The results of "Risk based, thresh = 0.001" with confidence bounds were estimated as the intercept of a mixed model that incorporated maps as a random effect and culling strategy as a fixed effect. The "+" or "-" for 1 km and 3 km ring culling indicate the difference compared to "Risk based, thresh = 0.001". Confidence bounds for 1 km and 3 km ring are also around the difference.

^{1) }In - > Out: culling starts with farms that are closest to the infected farm.

^{2) }Out - > In: culling starts with farms within the ring that are farthest from the infected farm.

There was substantial variation between the maps. Per map the relative improvement of risk based culling over ring culling remained approximately the same. The mean number of infected farms per map culled (across the three main strategies) ranged from 82 to 474, the total number of farms culled ranged from 956 to 1423, and the duration of the epidemic ranged from 53 to 64. The performance of each strategy per map was studied by carrying out an additional 2000 simulations per strategy, i.e. 40 for each map. On 6 out of 50 maps 1 km ring culling had a lower total number of farms culled than risk based culling, and 3 km ring culling gave a shorter epidemic on 5 maps. With the exception of these, risk based culling consistently outperformed 1 km and 3 km ring culling.

In the sensitivity analyses we investigated the effect of changes in culling capacity, reproduction number, tail of the hazard kernel, the level of clustering of farms, and a misspecified hazard kernel (Table

Preventive culling of farms is an important control measure to halt epidemics of highly infectious diseases of livestock such as classical swine fever, foot-and-mouth disease, and avian influenza. This paper introduces a novel prioritization scheme for culling of farms that is based on the idea that farms with the highest expected number of secondary infections should be culled first. Our simulations show that risk based culling outperforms ring culling in terms of the number of infected farms culled, the total number of farms culled, and the duration of the epidemic. As risk based culling reduced the number of infected farms that are culled it is therefore also expected to reduce the number of human infections. We find substantial variation in the outcome between different maps but for a given map risk based culling consistently outperformed ring culling. This indicates that the spatial structure has a large influence on the outcome of an epidemic, which is supported by previous research [

Although the model presented here is parameterised for the avian influenza epidemic that occurred in The Netherlands in 2003, the methodology of risk based culling is more generally applicable to other infectious diseases controlled by culling. The only information needed are the locations of the farms, the moments at which infected farms were culled (both essential for any control and usually available from surveillance), and an estimate of the distance-dependent probability of transmission. An extension of our method that could potentially further improve risk based culling would be to not only focus on the expected number of infections within one infection generation, but try to estimate the expected number of infections in second and perhaps even third infection generations in the future.

We assumed that all farms are equally infectious which is reasonable for avian influenza [

It is possible with an extensive misspecification in, for example, the infectivity of farms that risk based culling would be less effective. Note though that alternative strategies (such as ring culling) may suffer similarly. The challenge here is to have a good epidemiological understanding of how a disease spreads and incorporate this knowledge into the calculations. We believe that if misspecifications are minor, the reproductive number still identifies patches of farms that are close together weighted by their distance to infected farms. Quantitatively the outcomes may differ to some extent but qualitatively (risk based culling is about prioritizing) they may still be accurate. The effectiveness of risk based culling also depends on the culling capacity relative to the spread of disease. If the culling capacity is too low any control is impossible. If the culling capacity is very high then the order of culling becomes irrelevant. In between these extremes, culling resources need to be used efficiently and risk based culling can aid in this.

One advantage of risk based culling is that it does not require a certain arbitrary ring to be set. It can be argued however that the threshold needed in risk based culling to set the minimum risk level for culling is also arbitrary, and there is indeed not one clear risk based threshold (

For policy makers our risk based culling policy may be more difficult to justify to stake holders and the public than the simple traditional ring culling strategy. In addition, to be acceptable any culling strategy would have to satisfy the requirements of regulatory bodies. An intuitively appealing strategy may be to apply a risk based prioritization scheme within a culling ring. In our results this proved to be quite efficient (as shown in Table

In the past mainly ring culling strategies have been considered in practice and literature [

The authors declare that they have no competing interests.

DB, JS, MK, MB conceived the study, TH, MB, DB formulated the model equations, DB programmed the model, carried out the simulations, and drafted the manuscript. All authors read, amended and approved the final manuscript.

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This work was supported by CDC under the grant agreement U19 CI000404-01, Avian influenza collaborative research centers, Studies at the human animal interface, by the "Impulse Veterinary Avian Influenza Research in The Netherlands" program of the Dutch government, and by the Strategic Research theme Infectious Disease Dynamics of the Dutch National Institute of Public Health and the Environment. We would like to thank Jacco Wallinga for his input, and Jan van de Kassteele for his statistical advice.